Solids Friction Factors for Fluidized Dense-Phase Conveying

There have been numerous correlations proposed for determining a solids friction factor ( λs ) for fully suspended (dilute phase) pneumatic conveying. Currently, there are no equivalent correlations that predict λs in nonsuspension dense-phase flows. In dense-phase conveying there are two basic modes of flow: plug/slug flow, which is predominantly based on granular products, and fluidized dense-phase flow, which is more suited to fine powders exhibiting good air retention capabilities. In plug/slug type flow, the stresses between the moving plug of material and the pipe wall dominate the solid-phase frictional losses. In fluidized dense-phase flow the frictional losses are characterized as a mixture of particle-wall and particle-particle losses but are heavily influenced by the gas-solid interactions. In this paper, a series of calculations were performed on experimental data in order to estimate λs for four types of material conveyed in the fluidized dense-phase flow regime. The solids frictional factors were found to be relatively independent of particle properties for varying air and solid mass flow rates and pressure drops. The resultant pressure drop from the empirical model showed good agreement with the experimental data.     

A Simple Technique for Scaling Up Pneumatic Conveying Systems

A brief survey has shown that although scaling-up techniques in pneumatic conveying systems have generally been based on laboratory-scale test data, there still exists a divergence of opinions about the right choice of certain basic parameters such as solids friction factor and air friction factor. In this article, a simple model for pressure drop calculation has been proposed based on the classical Darcy's equation with some modifications. A parameter K, called pressure drop coefficient, has been shown to be independent of pipe diameter and hence suitable for scaling up to pipe sizes different from those used in laboratory-scale tests. For each of the bulk material and pipe size combinations used in this study, we calculated the standard deviation of predicted pressure values from the experimental values along the central 45° line passing through the origin; it varied from±165 mbar to a maximum±285 mbar. It has been shown that the model can be used for both horizontal and vertical pneumatic conveying.     

A Simple Technique for Scaling Up Pneumatic Conveying Systems

A brief survey has shown that although scaling-up techniques in pneumatic conveying systems have generally been based on laboratory-scale test data, there still exists a divergence of opinions about the right choice of certain basic parameters such as solids friction factor and air friction factor. In this article, a simple model for pressure drop calculation has been proposed based on the classical Darcy's equation with some modifications. A parameter K, called pressure drop coefficient, has been shown to be independent of pipe diameter and hence suitable for scaling up to pipe sizes different from those used in laboratory-scale tests. For each of the bulk material and pipe size combinations used in this study, we calculated the standard deviation of predicted pressure values from the experimental values along the central 45° line passing through the origin; it varied from±165 mbar to a maximum±285 mbar. It has been shown that the model can be used for both horizontal and vertical pneumatic conveying.     

太阳能电池阵地面展开试验的仿真技术

根据太阳能电池阵在地面展开试验条件下的受力状态,提出了蜗卷弹簧、空气阻力、气浮平台摩擦力、铰链副阻力矩等受力条件的定量计算方法,利用Lagrange方程建立了电池阵展开过程的动力学方程,由此对太阳能电池阵的地面展开试验进行了动力学仿真。对于空气阻力,提出了利用空气流场的动能表征阻力矩的简化处理方法,即空气阻力矩正比于广义附加质量的模型。     

Analysis of Gas-Solids Feeding and Slug Formation in Low-Velocity Pneumatic Conveying

Gas and solids feeding is a key operation in pneumatic conveying of particulate materials. This article presents an analysis of the interfacing effects between a nozzle gas supplier, a rotary valve solids feeder with dropout box, and the pipeline of a pneumatic conveying test rig for low-velocity dense-phase flow. Experiments were carried out to examine the flow pattern of slugs in different combinations of gas flow conditions and solids loading ratios. The effect of gas and solids feeding on the formation of slugs is analyzed by using both experimental data and computer-modeled results. Solids accumulation and sliding motion at the bottom of the dropout box and near the entrance of the downstream pipe, which happen prior to the bulk motion in the form of a slug, are found important in determining the size of a slug. Gas retention and pressure buildup characteristics in the feed section are also found crucial in influencing the flow patterns of slugs.     

Frictional behavior of granular gravel–ice mixtures in vertically rotating drum experiments and implications for rock–ice avalanches

Rapid mass movements involving large proportions of ice and snow can travel significantly further downslope than pure rock avalanches and may transform into debris-flows as the ice melts and as water from the stream network or water-saturated debris is incorporated. Currently, ice is thought to have three distinctive effects: 1) reduction of the friction within the moving mass itself, 2) increase of pore pressure as the ice melts and consequent reduction of the shear resistance of the flowing material, and 3) reduction of boundary friction where the failing mass travels on a glacier. However, measurement-based evidence to support these hypotheses is largely missing. In this study, laboratory experiments on the first two mechanisms were carried out in two partially-filled large rotating drums, one in Vienna (Austria) and a second in Berkeley (USA). Varying proportions of cold gravel and gravel-sized ice were mixed and added to the rotating drum running at constant rotational velocity until all ice had melted. Flow behavior was recorded with flow depth, normal force, shear force, pore-water pressure, and temperature sensors. The bulk friction coefficient was found to decrease linearly with increasing ice content by ~ 20% in the early phase of the experiments, before significant portions of the ice transformed into water. For ice contents larger than 40% by volume, the transformation from a dry granular flow to debris-flow-like movement or hyperconcentrated flow was observed when pore-water pressures rose and approached the normal forces along the flow profile. Pore-water pressure from melting ice developed within several minutes after the start of the experiments and, as it increased, progressively reduced the friction coefficient. The results emphasize that the presence of ice in granular moving material can significantly reduce the friction coefficient of both dry and partially-saturated debris. Due to size effects and the absence of other factors reducing friction (e.g. surfaces with low friction and rock comminution), the absolute measured friction coefficients from the laboratory experiments were larger than those found from natural events. However, the relative changes in friction coefficients depending on the ice and water content may also be considered in real-scale hazard assessments of rapid mass movements in high mountain environments.     

小麦颗粒弯管流动特性数值模拟研究

目的 为研究小麦颗粒在弯管处的气力输送的特性。方法 以欧拉-欧拉双流体模型为基础,结合壁面碰撞摩擦模型、颗粒动理学的固体应力和Gidaspow曳力模型构建出小麦颗粒在弯管处的气力输送模型,采用FLUENT对弯管处小麦颗粒气力输送过程进行数值模拟,分析小麦颗粒在流经弯管过程中及弯管后直管中的小麦颗粒密度分布、气固两相速度、小麦颗粒与壁面剪切力和颗粒相湍动能。结果 经过仿真分析和实验验证,小麦颗粒在流经弯管过程中,其颗粒相体积分数、气固两相速度、颗粒和壁面剪切力以及颗粒相湍动能4个方面随着流入弯管的角度变化而改变;由于颗粒-颗粒、颗粒-管壁之间的碰撞摩擦,小麦颗粒在流出弯管后随着输送距离的增大其各项参数逐渐减缓。结论 采用FLUENT软件进行仿真得到了弯管内小麦颗粒的流动特性,并通过实验验证了仿真的可靠性。此次研究结合气固两相理论,为弯管气力输送设计的研发和优化提供了理论基础。     

不同运动副材料对间隙机构动力学特性的影响

研究不同运动副材料对间隙机构动力学特性的影响。在考虑库仑摩擦的条件下,利用非线性等效弹簧阻尼的概念建立了含间隙运动副的接触动力学模型。在此基础上,利用动力学分析软件ADAMS考查了运动副材料不同时间隙机构动力学性能的变化。分析结果表明材料不同时运动副的摩擦、刚度和阻尼等因素均能影响机构的动力学性能,因此在设计时要加以考虑以提高机构性能并减少能量损失。     

浮置板道床非线性动力特性分析

本文针对新型的浮置板减振轨道，建立了具有三次非线性和Coulomb摩擦阻尼的的动力学模型，利用Fourier级数法和谐波平衡法，研究了列车荷载作用下浮置板轨道系统的频率响应特性，通过对弹簧刚度、阻尼等参数的研究，分析了系统参数对浮置板轨道减振特性的影响，并应用能量守恒方法研究了稳态响应的稳定性。     

轮轨横向滑动稳定性对曲线啸叫噪声的影响

车轮相对于钢轨发生横向滑动时,轮轨接触面上的摩擦力变化会引起曲线啸叫噪声。因此首先建立了车轮的状态空间模型和轮轨接触摩擦模型,对轮轨横向接触过程采用4阶Runge-Kutta法进行了时域分析,研究了如横向滑动速度、接触力、阻尼等因素对滑动过程稳定性的影响,并结合实例计算进行了验证,最终得出结论:轮轨横向滑动过程出现不稳定的主要原因是接触面间摩擦系数变化引起的自激振动;当车轮阻尼大于等效阻尼临界值时会使滑动过程稳定;轮轨间的垂向刚度和阻尼会使系统不稳定频率与车轮模态频率产生偏移。     

Attrition of Bulk Solids in Pneumatic Conveying: Mechanisms and Material Properties

In the approach presented, attrition of bulk solids in pneumatic conveying is regarded as a result of a process function (stress conditions) and a material function (influence of material properties). The paper focuses on dilute phase conveying (homogeneous flow) and in the first part describes the determination of the process function by employing computational fluid dynamics (CFD). In the second part, experimental results for the determination of the material function by means of simulating the previously identified stress modes of impact and friction under well-defined stress conditions are presented. Contrary to what was expected initially, the numerical simulations as well as experimental results indicate that sliding friction is apparently of importance in dilute phase conveying. This conclusion can be drawn from the low calculated impact angles in a pipe bend (r B /D=5; D=80 mm), which lie between 10 and 35°. Consequently, the tangential impact velocity components ranging from 32 to 40 m/s are considerably higher than the normal ones (5 to 22 m/s). These results are confirmed by observations made in experiments to determine the material function. The relative attrition behavior of four different polypropylenes under pure sliding friction conditions closely resembles that observed in attrition experiments carried out in a pipe bend of the above geometry, while differences are observed for normal impact conditions.     

Attrition of Bulk Solids in Pneumatic Conveying: Mechanisms and Material Properties

In the approach presented, attrition of bulk solids in pneumatic conveying is regarded as a result of a process function (stress conditions) and a material function (influence of material properties). The paper focuses on dilute phase conveying (homogeneous flow) and in the first part describes the determination of the process function by employing computational fluid dynamics (CFD). In the second part, experimental results for the determination of the material function by means of simulating the previously identified stress modes of impact and friction under well-defined stress conditions are presented. Contrary to what was expected initially, the numerical simulations as well as experimental results indicate that sliding friction is apparently of importance in dilute phase conveying. This conclusion can be drawn from the low calculated impact angles in a pipe bend (r B /D=5; D=80 mm), which lie between 10 and 35°. Consequently, the tangential impact velocity components ranging from 32 to 40 m/s are considerably higher than the normal ones (5 to 22 m/s). These results are confirmed by observations made in experiments to determine the material function. The relative attrition behavior of four different polypropylenes under pure sliding friction conditions closely resembles that observed in attrition experiments carried out in a pipe bend of the above geometry, while differences are observed for normal impact conditions.     

Vibration-induced arching in a deep granular bed

Forced vertical vibration of a granular layer can drive flow phenomena such as heaping, convection, fluidization, densification, surface waves and arching. Food, mineral processing, and pharmaceuticals industries all utilize vibratory processes for the handling and transport of granular materials. Understanding how a granular material responds when subjected to vibration is essential for equipment design. Three-dimensional discrete element simulations have been used in this study to investigate the convective motion leading to arching in a vertically vibrated, deep granular bed. The undulating granular layer contains alternating regions that first compact and then relax. The dynamics of these regions may depend on material properties such as restitution and friction coefficients; as well as particle shape. The effects of these factors on the kinematics and dynamics of the arching pattern are investigated here. The arching pattern is found to arise from synchronised momentum transfer between the rise and fall of the deforming granular layer and horizontally travelling waves. The arching pattern was found to be stable across a broad range of restitution and friction levels and particle shapes. Particles with high restitution tend to disrupt the timing between the vertical and horizontal periodic flows and affect the stability of the pattern selection. Large friction results in shear resistance, higher bed pressures, lower bulk densities, and delays in the timing of the vertical and horizontal momentum transfer. Non-sphericity leads to increased dilation of the bed, slower sideways velocities, and increased loading on the floor and dissipation rate in the bed.     

A phenomenological law for complex granular materials from Mohr-Coulomb theory

Manipulating powders still entails some clumsy and risky operations even now in the middle of the fourth industrial revolution. This is because there is a lack of well-understood theory about granular matter due to its ravelled complexity. However, granular matter is the second most handled material by man after water and is thus ubiquitous in daily life and industry only after water. Since the eighteenth century, mechanical and chemical engineers have been striving to manage the many difficulties of grain handling, most of which are related to flow problems. Many continuum models for dense granular flow have been proposed. Herein, we investigated Mohr–Coulomb failure analysis as it has been the cornerstone of stress distribution studies in industrial applications for decades. This research gathers over 130 granular materials from several industrial sectors, as varied as cement and flour, including raw materials, food, pharmaceuticals, and cosmetics. A phenomenological law derived from the yield locus and governed exclusively by one dimensionless number from adhesive interactions has been found. Surprisingly, and in contrast to the common perception, flow in the quasi-static regime is actually independent of the friction, the packing fraction and any other grains/bulk intrinsic properties. The simplicity and accuracy of the model are remarkable in light of the complex constitutive properties of granular matter.     

Frictionless conveying of frictional materials

Following a brief review of the technology and previous analyses of vibratory conveying of granular materials, a general solution is derived for a well-known rigid-slab model of slide-conveying in open and closed conduits, with Coulomb friction at the walls. The solution is applied to periodic rectangular-wave and sinusoidal forcing, and it is shown that the rectangular-wave forcing admits ideal cycles in which the kinematically optimal transport is also thermodynamically optimal, in the sense that no energy is dissipated by sliding friction.     

边界摩擦条件下含有预紧的对合碟簧隔振单元的振动特性

为研究对合碟簧的摩擦对隔振单元振动特性的影响,设计了一种存在预紧的对合碟簧隔振单元,建立了考虑边界摩擦条件下对合碟簧组的刚度模型。通过准静态加载试验验证了该刚度模型的正确性;并提出了该碟簧隔振单元的非线性动力学模型,应用平均法对对合碟簧隔振单元的自由振动进行分析,得出影响系统自由振动频率的各项因素;对基础激励下对合碟簧隔振单元的受迫振动进行分析计算。结果表明:在小位移振动条件下,该碟簧隔振单元可近似等效成非线性黏性阻尼系统,且附加支持力系数仅影响系统脱离频率,刚度三次项系数值的选取越大越不利于系统隔振;在大位移振动条件下,计算得到了系统存在异常跳跃状态与全频域内传递率系数T′d≤0状态,并说明这两种状态与黏性阻尼系数以及附加支持力系数间的联系。     

Frictional contact of flexible and rigid bodies

 This paper is about planar frictional contact problems of both flexible and rigid bodies. For the flexible case a nonlinear finite element formulation is presented, which is based on a modified Coulomb friction law. Stick-slip motion is incorporated into the formulation through a radial return mapping scheme. Linearly interpolating four node elements and three node contact elements are utilized for the finite element discretization. The corresponding tangent stiffness matrices and residual vectors of the equations of motion are presented. In the rigid body case the contact problem is divided into impact and continual contact, which are mathematically described by linear complementarity problems. The impact in normal direction is modeled by a modified Poisson hypothesis, which is adapted to allow multiple impacts. The formulation of the tangential impact is grounded on Coulombs law of friction. The normal contact forces of the continual contact are such that colliding bodies are prevented from penetration and the corresponding tangential forces are expressed by Coulombs law of friction. Examples and comparisions between the different methods are presented. Received: 10 January 2001     

An investigation of segregation and mixing in dense phase pneumatic conveying

Pneumatic conveying of bulk materials has become an important technology in many industries: from pharmaceuticals to petro-chemicals and power generation. Particulate segregation has been investigated in many solids handling processes. However, little work has been published on the segregation and mixing in pneumatic conveying pipelines, particularly in dense phase pneumatic conveying. Due to the character of dense phase flow, it is difficult to investigate the segregation in a flowing plug. A sampling device was designed and built to take samples from the pneumatic conveying pipeline after “catching a plug”. Several experiments were conducted over a range of gas–solids flow conditions with 3 mm nylon pellets and 3 mm ballotini as a segregating mixture. Experimental data combined with video footage were analysed to describe the segregation and mixing of solids plugs in pipes. This investigation provides initial research on establishing a segregation index in a flowing plug. A gas–solids two-dimensional mathematical model was developed for plug flow of a nylon-glass particulate mixture in a horizontal pipeline in dense phase pneumatic conveying. The model was developed based on the discrete element method (DEM). The model was used to simulate the motion of particles both in a homogeneous flow and as binary mixtures taking into account the various interactions between gas, particles and pipe wall. For the gas phase, the Navier Stokes equations were integrated by the semi-implicit method for pressure-linked equations (SIMPLE) using the scheme of Patankar employing the staggered grid system. For the particle motion the Newtonian equations of motion of individual particles were integrated, where repulsive and damping forces for particle collision, the gravity force, and the drag force were taken into account. For particle contact, a model with a simple non-linear spring and dash pot model for both normal and tangential components was used. This model employed a mixture of 3 mm pellets and ballotini as virtual materials with properties of nylon and glass. The results from the model are discussed and compared with experimental work and show qualitative agreement. Further modelling and experimental work in key areas is proposed.     

Flow–obstacle interaction in rapid granular avalanches: DEM simulation and comparison with experiment

This paper investigates the interaction between rapid granular flow and an obstacle. The distinct element method (DEM) is used to simulate the flow regimes observed in laboratory experiments. The relationship between the particle properties and the overall flow behaviour is obtained by using the DEM with a simple linear contact model. The flow regime is primarily controlled by the particle friction, viscous normal damping and particle rotation rather than the contact stiffness. Rolling constriction is introduced to account for dispersive flow. The velocity depth-profiles around the obstacles are not uniform but varying over the depth. The numerical results are compared with laboratory experiments of chute flow with dry granular material. Some important model parameters are obtained, which can be used to optimize defense structures in alpine regions.     

Flow properties of granular materials with large overburden loads

Summary For the rapid shear flow of granular materials with large overburden loads, an action involving the simultaneous impact of more than two particles is shown to provide a mechanism for reducing the effective drag force acting on the flowing material. The drag is reduced below both the static friction value and the drag due only to binary collisions. Since the frequency of multiparticle collisions increase as the bulk density of the flowing material decreases, larger overburdens result in more multiparticle collisions giving rise to greater decreases in the effective drag force. It is hypothesized that this mechanism may account for the extraordinarily long runout distances observed for large rockslides and avalanches. A simple numerical model of interacting inelastic disks in a quasi-two dimensional flow was used to guide the investigation and verify the proposed mechanism.With 5 Figures